To the Theory of $$\mathsf{H}$$-Sober Spaces: II. Approximation Spaces

We consider generalized sobrifications of approximation spaces and establish that they can be obtained as spaces of basic ideals defined on basic subspaces of the given spaces. As a consequence, we derive generalizations of a series of results on classical sobrifications of approximation spaces. In particular, we show that certain generalized sobrifications of such spaces are homeomorphic to their $$d$$ -completions.